Bus route planning is a challenging task due to multiple perspective interactions among passengers, service providers, and government agencies. This paper presents a multidimensional Stackelberg-game-based framework and mathematical model to best trade off the decisions of multiple stakeholders that previous literature rarely captures, i.e., governments, service providers, and passengers, in planning a new bus route or adjusting an existing one. The proposed model features a bilevel structure with the upper level reflecting the perspective of government agencies in subsidy allocation and the lower level representing the decisions of service providers in dispatching frequency and bus fleet size design. The bilevel model is framed as a Stackelberg game where government agencies take the role of “leader” and service providers take the role of “follower” with social costs and profits set as payoffs, respectively. This Stackelberg-game-based framework can reflect the decision sequence of both participants as well as their competition or collaboration relationship in planning a bus route. The impact of such decisions on the mode and route choices of passengers is captured by a Nested Logit model. A partition-based bisection algorithm is developed to solve the proposed model. Results from a case study in Shanghai validate the effectiveness and performance of the proposed model and algorithm.
Efficient fleet size optimization for task allocation of multiple unmanned vehicles
